Geodesic
On the core of a unicyclic graph
Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 325-331.

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A set S ⊆ V is independent in a graph G = (V, E) if no two vertices from S are adjacent. By core(G) we mean the intersection of all maximum independent sets. The independence number α(G) is the cardinality of a maximum independent set, while μ(G) is the size of a maximum matching in G. A connected graph having only one cycle, say C, is a unicyclic graph. In this paper we prove that if G is a unicyclic graph of order n and n − 1 = α(G) + μ(G), then core(G) coincides with the union of cores of all trees in G − C.
DOI : 10.26493/1855-3974.201.6e1
Keywords: maximum independent set, core, matching, unicyclic graph, Konig-Egervary graph 
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Vadim E. Levit; Eugen Mandrescu. On the core of a unicyclic graph. Ars Mathematica Contemporanea, Tome 5 (2012) no. 2, pp. 325-331. doi : 10.26493/1855-3974.201.6e1. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.201.6e1/

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